A New Quantum Probability Theory, Quantum Information Functor and Quantum Gravity

Quantum information theory is an important branch of theoretical physics with important experimental applications and is much richer than the classical one. Nonetheless, it seems that there is no precise description for it and people usually refer to some special aspects which show the difference between these two theories like, for instance, the no cloning theorem. Our aim here is to propose a new definition of quantum information theory by means of category theoretic tools and then show it can be more “natural” than classical information theory in some respect. This definition also suggests that loop quantum gravity and string theory are two shapes of a same theory of quantum gravity which are describable as two different conceptions of space time and space in a special mathematical structure. This mathematical structure is topos. In addition, we claim that within this point of view information is more fundamental than the concepts of space and space time in physics. We got inspired from the works of John Baez to work on this subject.